Also notice that contrary to `standard' \(D=5\)  BHs [1]}Similar results have been obtained by Daniel Mayerson for BMPV BHs. We thank him for sharing his insights. no log terms are possible since they would be incompatible with regularity at \(z=0\)  and they cannot be generated by analytic continuation of \(R_{reg}(z) = z^{|m_\psi | \over 2} (1-z)^{|m_\phi | \over 2} F_r\) 
to infinity since \(F_r\)  is a polynomial. This is another feature that distinguishes (circular) fuzz-balls from (small) BHs even in the rigorously static limit.
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